A Commutattvity Theorem for Rings and Groups

Author:

Nicholson W. K.,Yaqub Adil

Abstract

AbstractThe following theorem is proved: Suppose R is a ring with identity which satisfies the identities xkyk = ykxk and xlyl = ylxl, where k and l are positive relatively prime integers. Then R is commutative. This theorem also holds for a group G. Furthermore, examples are given which show that neither R nor G need be commutative if either of the above identities is dropped. The proof of the commutativity of R uses the fact that G is commutative, where G is taken to be the group R* of units in R.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 10 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Commutativity Study for Certain Rings;Annals of the Alexandru Ioan Cuza University - Mathematics;2010-01-01

2. Commutativity for a certain class of rings;Georgian Mathematical Journal;1996-01

3. Some conditions for the commutativity of rings;Acta Mathematica Hungarica;1993-03

4. Commutativity theorems for s-unital rings with constraints on commutators;Results in Mathematics;1992-05

5. Commutativity of rings satisfying certain polynomial identities;Bulletin of the Australian Mathematical Society;1991-08

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